Colloidal quantum dots (CQDs) are nanoscale building blocks for bottom-up fabrication of semiconducting solids with tailorable properties beyond the possibilities of bulk materials. Achieving ordered, macroscopic crystal-like assemblies has been in the focus of researchers for years, since it would allow exploitation of the quantum-confinement-based electronic properties with tunable dimensionality. Lead-chalcogenide CQDs show especially strong tendencies to self-organize into 2D superlattices with micrometer-scale order, making the array fabrication fairly simple. However, most studies concentrate on the fundamentals of the assembly process, and none have investigated the electronic properties and their dependence on the nanoscale structure induced by different ligands. Here, it is discussed how different chemical treatments on the initial superlattices affect the nanostructure, the optical, and the electronic-transport properties. Transistors with average two-terminal electron mobilities of 13 cm V s and contactless mobility of 24 cm V s are obtained for small-area superlattice field-effect transistors. Such mobility values are the highest reported for CQD devices wherein the quantum confinement is substantially present and are comparable to those reported for heavy sintering. The considerable mobility with the simultaneous preservation of the optical bandgap displays the vast potential of colloidal QD superlattices for optoelectronic applications.